State estimation for gene networks with intrinsic and extrinsic noise: a case study on E.coli arabinose uptake dynamics

We address state estimation for gene regulatory networks at the level of single cells. We consider models that include both intrinsic noise, in terms of stochastic dynamics, and extrinsic noise, in terms of random parameter values. We take the Chemical Master Equation (CME) with random parameters as a reference modeling approach, and investigate the use of stochastic differential model approximations for the construction of practical real-time filters. To this aim we consider a Square-Root Unscented Kalman Filter (SRUKF) built on a Chemical Langevin Equation (CLE) approximation of the CME. Using arabinose uptake regulation in Escherichia coli bacteria as a case study, we show that performance is comparable to that of a (computationally heavier) particle filter built directly on the CME, and that the use of information about parameter uncertainty allows one to improve state estimation performance.